Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x + 1$ and $ JT = 2x + 15$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x + 1} = {2x + 15}$ Solve for $x$ $ 7x = 14$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({2}) + 1$ $ JT = 2({2}) + 15$ $ CJ = 18 + 1$ $ JT = 4 + 15$ $ CJ = 19$ $ JT = 19$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {19} + {19}$ $ CT = 38$